Aircraft: LARGE TRANSPORT
Phase of flight: Cruise
Anomaly: Aircraft Equipment Problem Critical; Deviation - Speed All Types; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Published Material / Policy

I was on the PF on the flight from ZZZ to ZZZ1. While in cruise flight at FL320 approximately in VMC and 50 miles east of the ZZZ VOR; the FMA displayed an amber 'HORIZON' light and a 'NO AUTOLAND' light. The autopilot remained engaged and initially we did not notice any other abnormal indications. The Captain and I discussed the situation and we began researching the problem in the QRH. As we researched the problem in the QRH and discussed the situation the amber 'HEADING' light illuminated on the FMA. The pitch indication on the First Officer (FO) Primary Flight Display (PFD) now indicated a 10 degree nose down pitch indication (actual flight was straight and level). We referred to the standby compass and determined the FO ND compass the Captain (CA) RMI headings also were incorrect by about 20 degrees.The autopilot remained engaged and appeared to be properly tracking to ZZZ. As we continued the ground speed on the FP PFD began increasing rapidly to 800+ knots and the GS on the ND indicated 275 knots on the tail. About 15 NM prior to the ZZZ VOR the airplane began a smart turn on the route in the FMS and we immediately selected heading and continued to assess the situation while attempting to track to ZZZ manually via the VOR on the RMI. ATC asked us our heading at the very time we were discussing our plan to communicate our malfunction with ATC.ATC gave us a heading to fly and shortly thereafter the autopilot; auto throttles disconnected and the FD disappeared. The FMAs went blank. We informed ATC of our capability losses and received guidance to descend from FL320 to FL280 where we remained until descending into ZZZ1. As we continued the MAP function on the FO ND failed and we received an MCDU message IRS Platform (2) Fail.A couple of times during the process of assessing the malfunction; reviewing the QRH and data; and communication process we transferred control back and forth. The CA PFD and ND appeared mostly normal so we selected EFIS display BOTH ON 1 and I continued to act as PF for the remainder of the flight. At some point the FD came back into view but the FD guidance appeared erroneous so we turned off the #1 PFD. At some point in the process we selected the DFGC #1 but that did not seem to change anything and the FD did not come into view. The CA ND/MAP appeared mostly normal for about 5 minutes after the FO ND became unreliable and it subsequently failed and we received a MCDU message IRS Platform (1) Fail.We continued to compare headings against the standby compass and flew via vectors towards ZZZ1. We determined out position using the VOR and compared that with the ATC known position. The FMS position was approximately 500 NM from our actual position (it was normal and the route positions and lengths all checked prior to Takeoff).We [advised ATC] in the process and the CA informed the company via flight phone of our situation and intentions. We elected to continue to ZZZ1 as we deemed the weather capable for a visual approach once we got below the weather on final.Descent into ZZZ1 was relatively uneventful and ATC set us up for a 10 mile final at 2100 feet. We were able to track inbound on the localizer manually (no FD) and monitor the glide slope manually (no FD). We broke out at 2300 feet and acquired the runway and flew a visual approach using the PAPI and ILS Manual GS information to a landing. While in cruise the FMA displayed an amber 'HORIZON' light and a 'NO AUTOLAND' light. The 'HEADING' light illuminated on the FMA. While in level flight; the pitch indication on the FO Primary Flight Director indicated a 10 degree nose down pitch. The FO Navigation Display compass and the Captains RMI headings also were incorrect by about 20 degrees. The ground speed on the FO PFD began increasing rapidly to 800+ knots and the Ground Speed on the ND indicated 275 knots. FO ND became unreliable and it subsequently failed then received a MCDU message IRS Platform (1) Fail.